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/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>

/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
{
  int ix, res, digs;
  mp_digit mu;

  /* can the fast reduction [comba] method be used?
*
* Note that unlike in mp_mul you're safely allowed *less*
* than the available columns [255 per default] since carries
* are fixed up in the inner loop.
*/
  digs = n->used * 2 + 1;
  if ((digs < MP_WARRAY) &&
      n->used <
      (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
    return fast_mp_montgomery_reduce (x, n, rho);
  }

  /* grow the input as required */
  if (x->alloc < digs) {
    if ((res = mp_grow (x, digs)) != MP_OKAY) {
      return res;
    }
  }
  x->used = digs;

  for (ix = 0; ix < n->used; ix++) {
    /* mu = ai * rho mod b
*
* The value of rho must be precalculated via
* bn_mp_montgomery_setup() such that
* it equals -1/n0 mod b this allows the
* following inner loop to reduce the
* input one digit at a time
*/
    mu = ((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK;

    /* a = a + mu * m * b**i */
    {
      register int iy;
      register mp_digit *tmpn, *tmpx, u;
      register mp_word r;

      /* alias for digits of the modulus */
      tmpn = n->dp;

      /* alias for the digits of x [the input] */
      tmpx = x->dp + ix;

      /* set the carry to zero */
      u = 0;
      
      /* Multiply and add in place */
      for (iy = 0; iy < n->used; iy++) {
        /* compute product and sum */
        r = ((mp_word)mu) * ((mp_word)*tmpn++) +
                  ((mp_word) u) + ((mp_word) * tmpx);

        /* get carry */
        u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

        /* fix digit */
        *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
      }
      /* At this point the ix'th digit of x should be zero */


      /* propagate carries upwards as required*/
      while (u) {
        *tmpx += u;
        u = *tmpx >> DIGIT_BIT;
        *tmpx++ &= MP_MASK;
      }
    }
  }

  /* at this point the n.used'th least
* significant digits of x are all zero
* which means we can shift x to the
* right by n.used digits and the
* residue is unchanged.
*/

  /* x = x/b**n.used */
  mp_clamp(x);
  mp_rshd (x, n->used);

  /* if x >= n then x = x - n */
  if (mp_cmp_mag (x, n) != MP_LT) {
    return s_mp_sub (x, n, x);
  }

  return MP_OKAY;
}
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